Problem: Simplify the following expression: $\sqrt{112} + \sqrt{63}$
Explanation: First, try to factor any perfect squares out of the radicals. $= \sqrt{112} + \sqrt{63}$ $= \sqrt{16 \cdot 7} + \sqrt{9 \cdot 7}$ Separate the radicals and simplify. $= \sqrt{16} \cdot \sqrt{7} + \sqrt{9} \cdot \sqrt{7}$ $= 4\sqrt{7} + 3\sqrt{7}$ Finally, simplify by combining the terms. $= ( 4 + 3 )\sqrt{7} = 7\sqrt{7}$